Catan – The Odds of Throwing Each Number

Herein lies the odds – plus the reason why it is so.

The Chances of Rolling Each Number

  • 2 … 2.8% (or 1 in 36)
  • 3 … 5.6% (or 2 in 36)
  • 4 … 8.3% (or 3 in 36)
  • 5 … 11.1% (or 4 in 36)
  • 6 … 13.9% (or 5 in 36)
  • 7 … 16.7% (or 6 in 36)
  • 8 … 13.9% (or 5 in 36)
  • 9 … 11.1% (or 4 in 36)
  • 10 … 8.3% (or 3 in 36)
  • 11 … 5.6% (or 2 in 36)
  • 12 … 2.8% (or 1 in 36)

You can see the number 7 shows up most often at 16.7% of the time, accompanied by the Robber. So it turns out you’re not just paranoid after all , the game really is out to get you!

How Come the Chances of Rolling Each Number Are So Different?

Check this out.

It shows that some numbers can get made out of a stack of many different dice combos (7 has a stack of 6 possible combos).

Other numbers are only formed from much fewer combos, so you chances of seeing them are much smaller (e.g. the numbers 2 and 12 can each be made from a only single dice combo), That’s why building next to the 2 and 12 numbered tiles is only for desperadoes.

The Dice Have No Memory

Wow, three 7’s in a row! The next roll has gotta be different right? Sadly this is the mistake made by many amateur gamblers looking for that ‘hot table’ that’s overdue to throw lots of their desired numbers.

This is because the available dice combos never get ‘used up’. (you could say each time you throw the dice the above chart of available combos ‘refreshes’). So regardless of what was thrown before, the odds of a 7 remain 16.7%.

Yes, reality is really just that disinterested you.


If you didn’t already know all this, you’re in good company. In the old days the great fortunes of noblemen were lost gambling at two-dice backgammon games. At least until some smart cookies worked out what was really going on. And with just that, they kicked off the whole maths field of probability.

Clearly then, mastering Settlers of Catan is a key step towards mastering probability theory. And probability theory is the very basis of Quantum Physics. Once fully understood, quantum physics will eventually unlock unlimited clean fusion energy, delaying the impending Apocalypse by centuries.

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